On the Singular Value Decomposition and Ranking Techniques

• Autorzy: Zizler P. , Thangarajah P. , Sobhanzadeh M.

Identyfikatory

DOI

10.12921/cmst.2019.0000048

• Języki publikacji: EN

Abstrakty

EN

Let A be a positive non-singular n×n matrix. An approximation for a positive eigenvector for A∗A corresponding to the dominant singular value of A was suggested as the normalized version of a weighted sum of the rows of A with weights being the euclidean norms of the rows of A. In our paper we give a justification for this approach via the iteration of the power method and we show numerically that choosing the l1 norm yields better results. Applications of our results are given to ranking techniques.

Słowa kluczowe

EN

singular value decomposition; positive matrices; ranking

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2020
• Tom: Vol. 26, No. 1
• Strony: 15--20
• Opis fizyczny: Bibliogr. 8 poz., rys.

Twórcy

autor

Zizler P.

• Mount Royal University 4825 Mt Royal Gate SW Calgary, AB T3E 6K6

autor

Thangarajah P.

• Mount Royal University 4825 Mt Royal Gate SW Calgary, AB T3E 6K6

autor

Sobhanzadeh M.

• Mount Royal University 4825 Mt Royal Gate SW Calgary, AB T3E 6K6

Bibliografia

• [1] G. Benettin, L. Galgani, A. Giorgilli, J.M. Strelcyn, Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; A method for computing all of them. Part 2: Numerical application, Meccanica 15, 21–30 (1980).
• [2] C. Hepler, P. Thangarajah, P. Zizler, Ranking in Professional Sports: An Application of Linear Algebra for Computer Science Students, 21st Western Canadian Conference on Computing Education, Kamloops, BC, Canada (2016).
• [3] R.A. Hanneman, M. Riddle, Concepts and Measures for Basic Network Analysis, The Sage Handbook of Social Network Analysis, SAGE, 346–347 (2011).
• [4] D. James, C. Botteron, Understanding Singular Vectors, The College Mathematics Journal 44(3), 220–226 (2013).
• [5] P. Lancaster, M. Tismenetsky, The Theory of Matrices, Academic Press (1985).
• [6] S. Montesinos, P. Zizler, V. Zizler, An Introduction to Modern Analysis, Springer (2015).
• [7] I. Shimada, T. Nagashima, A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems, Progress of Theoretical Physics 61(6), 1605–1616 (1979).
• [8] G. Strang, Linear Algebra and Its Applications, Cengage (previously Brooks/Cole), 4th edition (2006).

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).